Just Blame Fred

Back in 2000, I used to be a day trader full-time. Everyday I would watch the markets and attempt to capitalize on short term price movements. In order to “predict” those price movements, I would look at lots of data and news every day, and even wrote some software to analyze some of that time-series data to give me a kind of “forecast” for the trading day.

We all know about “price discovery”, being “overbought”, “oversold”, “retracements” and the like. A difference is assumed between the “investor” and the “trader”, even to the point of absolutionist morality. It is seen as a “good thing” by the general public to be an “investor”, and a “bad thing” to be a “trader”. There’s lots of misconceptions about the equities market, and a lot of those misconceptions are intentional by those who stand to gain from the general ignorance and folklore on the part of the public.

Ah yes. But if we didn’t have the “traders” in the market short-term, there would not be enough liquidity for the long-term “investors”. They need each other, it would seem.

But the real question what is really going on needs to be understood and answered to truly understand the equities market.

Firstly, one must understand the basic fundamentals of the equities market. It is a zero-sum game. Exchanges occurs between one trader and another; between one investor and another. The goal of anyone in the equities market — investor or trader — is to find a “greater fool” than oneself to buy the stock at a higher price than one’s “strike price”.

That is to say, that every dollar you make in the equities market came at the expense of someone else, and every dollar you loose in the equities market  goes in somebody’s pocket.

This is a very tough concept for some to accept, because if you listen to all the spin about the equities market, you are lead to believe that the wealth one could supposedly make happens by “magic”. It does not. It happens at the expense of other players in the market.

That reality is played out — rather painfully — by the market “crashes” such as the one we are having now,  where so many loose their “investment”. They are paying for the profit of others before them. Plain and simple. And the sad reality of this is that prices will not rise again until the greatest fools of all jump out of the market in sheer panic and terror.

Indeed, it is a requirement for this to happen. Prices must fall. The giveback must occur. The Faustian bargain must be paid in full. This is the mathematical reality of a zero-sum game.

After you understand and appreciate the inanity of this, consider it even more insane that many are encouraged to put their retirement investments in the equities market.

Why does this happen? Simple. Because the supply of fools are finite, and to carry the market higher so for the Big Players to make a profit, they must suck in legions of smaller fools who don’t know any better.

The party works for a while. The more fools you suck in, the higher the prices are driven. Until, of course, you hit a wall and are unable to suck in anymore fools. Then the prices fall mercilessly, and many see their hard-earned life’s wealth washed away into the pockets of others.

The media calls this a “loss”. It should really be called a “transfer”, because that’s exactly what it is — a transfer of wealth.

They are encouraged to “stay in so they can catch the next uptick”. The sad irony is, of course, that if they would all stay in as they are recommended to by the financial planners, the market would never rise again. It only rises when many jump out of the market, giving up their holdings at prices below their strike, to smarter fools that will simply lie in wait for the whole “Ponzi Scheme” to repeat itself.

Now, with that notion in our minds, we are now in a stronger position to understand the true psychodymanics of the equities market.

I have struggled for some time now to conceive of a good model for the stock market. My latest one goes like this: On a given day, a given stock trades in a limited range of prices, at a certain volume. That volume and price range represents new ownership of that stock at a range of strike prices for that day. Since it is not known who owns what, I turn the issue on its head, and consider each individual stock as its own owner.

Crazy, you say? Maybe. But why not? If one person bought 10,000 shares of XYZ, would not the psychology be more or less the same as though 10 people bought 1000 shares each of XYZ? Or a hundred people purchased 100 shares each?

You are starting to see the picture here. Of course, in actuality, the specific goals of 100 people will probably all be different from each other — some may be doing this in a retirement account; others may be day traders. Some may be a mutual funds management. But that’s the whole idea. If I consider each individual stock as its own owner, then I can assign “flocking behavior” to groups of XYZ that all behave the same way. it allows me to reduce the problem of ownership to its bare elements. If 10,000 shares of XYZ all behave the same way, does it really matter if it had one owner or 10,000 with the same mindset? No, it does not.

When a share is traded, it looses is past owner and has a new owner at a new strike price. So now you have two components to deal with — the strike price and the goal of each share of stock.

When a the market is trading above the strike price of a owned stock, that owner is said to be “happy”. If the market price is trading below the strike, that owner is said to be “sad”.  We can then assign some probability of “ownership flipping” to that stock based on its own goals of greed and fear and the expectation of price evolution.

We can generally state that the probability of ownership flipping increases as the market price moves away from the strike price. But the probability curve is not symmetric for “happy” stocks and “sad” stocks. The probability increases faster for “sad” stocks than it does for “happy” stocks. Also, the details of the dynamics of how the price moves away from the strike is important. Fast moves will increase the probability of a flip faster than slow moves.  Price moves in certain patterns may shift the probability faster than other patterns. External factors such as news will also have an effect on that probability of a flip. Then there are automatic trading systems and the like. The picture becomes rather complex.

Add to that the fact that a flip influences others to flip. One single flip could trigger an avalanche of flips. This is self-organized criticality speaking here.

Now, it is clear that we, for the most part, have no ready access to the ownership space and distribution of the market capitalization of an equity at any given point in time. However, we do have a print of past history of stock price ranges and volumes for fixed intervals (minutes, hours, days, weeks, months, years).

So, for any given time period p, where volume v of stock activity occurred, we know that at most v shares of stock are owned over the price range of p. We also know that at least min(t) shares are owned, t being the number of shares traded of a single tick over p. But this amount is so small in comparison that we can safely assume that w — the number of shares flipped during p — will be much larger than min(t) — that is, v >= w >> min(t).

For simplicity, we will simply ignore, for the moment, the possibility of shares flipping multiple times during p, as would be the case with day traders. We will also ignore shorting, but will treat it later.

So, given p₁, p₂, …, p_n, we have D₁, D_{лаптоп2}, …, D_n, where D_i = D(p_i), price distribution for period p_i. Of course, D shall be confined to the price range of the associated period. We also have ξ, the complete set of stock ownership for a given equity, where D_i is a subset that is dynamic on i.